Problem: What is the extraneous solution to these equations? $\dfrac{x^2 - 9x}{x - 2} = \dfrac{8x - 70}{x - 2}$
Solution: Multiply both sides by $x - 2$ $ \dfrac{x^2 - 9x}{x - 2} (x - 2) = \dfrac{8x - 70}{x - 2} (x - 2)$ $ x^2 - 9x = 8x - 70$ Subtract $8x - 70$ from both sides: $ x^2 - 9x - (8x - 70) = 8x - 70 - (8x - 70)$ $ x^2 - 9x - 8x + 70 = 0$ $ x^2 - 17x + 70 = 0$ Factor the expression: $ (x - 7)(x - 10) = 0$ Therefore $x = 7$ or $x = 10$ The original expression is defined at $x = 7$ and $x = 10$, so there are no extraneous solutions.